{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Presentation.ipynb",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/VIGNESHinZONE/Beginners-level-ML-projects/blob/master/Presentation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PTCDW4wAZ3_A",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9b6544af-4267-4fc4-fe88-3cd6e766f89b"
      },
      "source": [
        "!pip install --pre deepchem[jax]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting deepchem[jax]\n",
            "  Downloading deepchem-2.6.0.dev20210924223259-py3-none-any.whl (609 kB)\n",
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            "\u001b[?25hRequirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from deepchem[jax]) (1.4.1)\n",
            "Requirement already satisfied: scikit-learn in /usr/local/lib/python3.7/dist-packages (from deepchem[jax]) (0.22.2.post1)\n",
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            "Requirement already satisfied: joblib in /usr/local/lib/python3.7/dist-packages (from deepchem[jax]) (1.0.1)\n",
            "Collecting optax\n",
            "  Downloading optax-0.0.9-py3-none-any.whl (118 kB)\n",
            "\u001b[K     |████████████████████████████████| 118 kB 52.6 MB/s \n",
            "\u001b[?25hRequirement already satisfied: jaxlib in /usr/local/lib/python3.7/dist-packages (from deepchem[jax]) (0.1.71+cuda111)\n",
            "Collecting dm-haiku\n",
            "  Downloading dm_haiku-0.0.5.dev0-py3-none-any.whl (284 kB)\n",
            "\u001b[K     |████████████████████████████████| 284 kB 30.1 MB/s \n",
            "\u001b[?25hRequirement already satisfied: jax in /usr/local/lib/python3.7/dist-packages (from deepchem[jax]) (0.2.21)\n",
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            "Collecting chex>=0.0.4\n",
            "  Downloading chex-0.0.8-py3-none-any.whl (57 kB)\n",
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            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.7/dist-packages (from pandas->deepchem[jax]) (2018.9)\n",
            "Installing collected packages: chex, optax, dm-haiku, deepchem\n",
            "Successfully installed chex-0.0.8 deepchem-2.6.0.dev20210924223259 dm-haiku-0.0.5.dev0 optax-0.0.9\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LfD5vWN7aFPl"
      },
      "source": [
        "import numpy as np\n",
        "import functools\n",
        "try:\n",
        "  import jax\n",
        "  import jax.numpy as jnp\n",
        "  import haiku as hk\n",
        "  import optax\n",
        "  from deepchem.models import PINNModel, JaxModel\n",
        "  from deepchem.data import NumpyDataset\n",
        "  from deepchem.models.optimizers import Adam\n",
        "  from jax import jacrev\n",
        "  has_haiku_and_optax = True\n",
        "except:\n",
        "  has_haiku_and_optax = False\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "duz1qOjUKqwn"
      },
      "source": [
        "\n",
        "\n",
        "# Given Physical Data\n",
        "\n",
        "We have a 10 random points between $x\\in [-2\\pi, 2\\pi]$ and its corresponding value f(x)\n",
        "\n",
        "We know that data follows an underlying physical rule that\n",
        "\n",
        "$\\frac{df(x)}{dx} = -sin(x) $\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C4qgTvtvRYCH",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "outputId": "34dff467-b962-44e9-fad6-de240d33d20e"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "give_size = 10\n",
        "in_given = np.linspace(-2 * np.pi, 2 * np.pi, give_size)\n",
        "out_given = np.cos(in_given) + 0.1*np.random.normal(loc=0.0, scale=1, size=give_size)\n",
        "\n",
        "\n",
        "\n",
        "# red for numpy.sin()\n",
        "plt.figure(figsize=(13, 7))\n",
        "\n",
        "plt.scatter(in_given, out_given, color = 'green', marker = \"o\")\n",
        "plt.xlabel(\"x --> \", fontsize=18)\n",
        "plt.ylabel(\"f (x) -->\", fontsize=18)\n",
        "plt.legend([\"Supervised Data\"], prop={'size': 16}, loc =\"lower right\")\n",
        "\n",
        "plt.title(\"Data of our physical system\", fontsize=18)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Data of our physical system')"
            ]
          },
          "metadata": {},
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XmlpOmyFNVCy"
      },
      "source": [
        "From simple integeration, we can easily solve the diffrential equation and the solution will be - \n",
        "\n",
        "$f(x) = cos(x)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gc02TT21L3VX",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "outputId": "3c668ae6-2c4a-4588-d6dd-d01a0d9e03b7"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "test = np.expand_dims(np.linspace(-2.5 * np.pi, 2.5 * np.pi, 100), 1)\n",
        "out_array = np.cos(test)\n",
        "\n",
        "plt.figure(figsize=(13, 7))\n",
        "plt.plot(test, out_array, color = 'blue', alpha = 0.5)\n",
        "plt.scatter(in_given, out_given, color = 'green', marker = \"o\")\n",
        "plt.xlabel(\"x --> \", fontsize=18)\n",
        "plt.ylabel(\"f (x) -->\", fontsize=18)\n",
        "plt.legend([\"Actual data\" ,\"Supervised Data\"], prop={'size': 16}, loc =\"lower right\")\n",
        "\n",
        "plt.title(\"Data of our physical system\", fontsize=18)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Data of our physical system')"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7ze0wpglNwja"
      },
      "source": [
        "# Building a Simple Neural Network Model - \n",
        "\n",
        "We define a simple Feed-forward Neural Network with 2 hidden layers of size 256 & 128 neurons."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IdBSG-h2ahxE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5a6ab90f-0250-4e7b-e50e-7357a2fb436c"
      },
      "source": [
        "# defining the Haiku model\n",
        "\n",
        "# A neural network is defined as a function of its weights & operations.\n",
        "# NN(x) = F(x, W) \n",
        "\n",
        "# forward function defines the F which describes the mathematical operations like Matrix & dot products, Signmoid functions, etc\n",
        "# W is the init_params\n",
        "\n",
        "def f(x):\n",
        "  net = hk.nets.MLP(output_sizes=[256, 128, 1], activation=jax.nn.softplus)\n",
        "  val = net(x)\n",
        "  return val\n",
        "\n",
        "init_params, forward_fn = hk.transform(f)\n",
        "rng = jax.random.PRNGKey(500)\n",
        "params = init_params(rng, np.random.rand(1000, 1))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py:3634: UserWarning: Explicitly requested dtype float64 requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
            "  lax._check_user_dtype_supported(dtype, \"zeros\")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2wjlvQg2ODjT"
      },
      "source": [
        "# Fitting a simple Neural Network solution to the Physical Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AU6pQC_8V4Pf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4d0baed8-7d72-4540-f7bb-892f9b44701f"
      },
      "source": [
        "\n",
        "train_dataset = NumpyDataset(np.expand_dims(in_given, axis=1), np.expand_dims(out_given, axis=1))\n",
        "rms_loss = lambda pred, tar, w: jnp.mean(optax.l2_loss(pred, tar))\n",
        "# JaxModel Working\n",
        "nn_model = JaxModel(\n",
        "    forward_fn,\n",
        "    params,\n",
        "    rms_loss,\n",
        "    batch_size=100,\n",
        "    learning_rate=0.001,\n",
        "    log_frequency=2)\n",
        "nn_model.fit(train_dataset, nb_epochs=10000, deterministic=True)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/deepchem/models/jax_models/jax_model.py:160: UserWarning: JaxModel is still in active development and all features may not yet be implemented\n",
            "  'JaxModel is still in active development and all features may not yet be implemented'\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.1729056921826473e-11"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TA-EWXjaYvoG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "outputId": "fd21bc93-594e-4bc0-9120-f3ed60fe9187"
      },
      "source": [
        "dataset_test = NumpyDataset(test)\n",
        "nn_output = nn_model.predict(dataset_test)\n",
        "\n",
        "plt.figure(figsize=(13, 7))\n",
        "plt.plot(test, out_array, color = 'blue', alpha = 0.5)\n",
        "plt.scatter(in_given, out_given, color = 'green', marker = \"o\")\n",
        "plt.plot(test, nn_output, color = 'red', marker = \"o\", alpha = 0.7)\n",
        "plt.xlabel(\"x --> \", fontsize=18)\n",
        "plt.ylabel(\"f (x) -->\", fontsize=18)\n",
        "plt.legend([\"Actual data\", \"Vanilla NN\", \"Supervised Data\"], prop={'size': 16}, loc =\"lower right\")\n",
        "\n",
        "plt.title(\"Data of our physical system\", fontsize=18)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Data of our physical system')"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_1aFyjksOL8i"
      },
      "source": [
        "# Learning to fit the Data using the underlying Diffrential equation\n",
        "\n",
        "Lets ensure that final output of the neural network satisfies the diffrential equation as a loss function- "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ALDGNdBhCTy8"
      },
      "source": [
        "def create_eval_fn(forward_fn, params):\n",
        "  \"\"\"\n",
        "    Calls the function to evaluate the model\n",
        "  \"\"\"\n",
        "\n",
        "  @jax.jit\n",
        "  def eval_model(x, rng=None):\n",
        "\n",
        "    bu = forward_fn(params, rng, x)\n",
        "    return jnp.squeeze(bu)\n",
        "\n",
        "  return eval_model\n",
        "\n",
        "def gradient_fn(forward_fn, loss_outputs, initial_data):\n",
        "  \"\"\"\n",
        "  This function calls the gradient function, to implement the backpropagation\n",
        "  \"\"\"\n",
        "  boundary_data = initial_data['X0']\n",
        "  boundary_target = initial_data['u0']\n",
        "\n",
        "  @jax.jit\n",
        "  def model_loss(params, target, weights, rng, x_train):\n",
        "\n",
        "    @functools.partial(jax.vmap, in_axes=(None, 0))\n",
        "    def periodic_loss(params, x):\n",
        "      \"\"\"\n",
        "      diffrential equation => grad(f(x)) = - sin(x)\n",
        "      minimize f(x) := grad(f(x)) + sin(x)\n",
        "      \"\"\"\n",
        "      x = jnp.expand_dims(x, 0)\n",
        "      u_x = jacrev(forward_fn, argnums=(2))(params, rng, x)\n",
        "      return u_x + jnp.sin(x)\n",
        "\n",
        "    u_pred = forward_fn(params, rng, boundary_data)\n",
        "    loss_u = jnp.mean((u_pred - boundary_target)**2)\n",
        "\n",
        "    f_pred = periodic_loss(params, x_train)\n",
        "    loss_f = jnp.mean((f_pred**2))\n",
        "\n",
        "    return loss_u + loss_f\n",
        "\n",
        "  return model_loss\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3VLC2gTsaVzU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e9840ac1-b1fa-49a8-fceb-8280e6f2e84f"
      },
      "source": [
        "\n",
        "\n",
        "\n",
        "initial_data = {\n",
        "    'X0': jnp.expand_dims(in_given, 1),\n",
        "    'u0': jnp.expand_dims(out_given, 1)\n",
        "}\n",
        "opt = Adam(learning_rate=1e-3)\n",
        "pinn_model= PINNModel(\n",
        "    forward_fn=forward_fn,\n",
        "    params=params,\n",
        "    initial_data=initial_data,\n",
        "    batch_size=1000,\n",
        "    optimizer=opt,\n",
        "    grad_fn=gradient_fn,\n",
        "    eval_fn=create_eval_fn,\n",
        "    deterministic=True,\n",
        "    log_frequency=1000)\n",
        "\n",
        "# defining our training data. We feed 100 points between [-2.5pi, 2.5pi] without the labels,\n",
        "# which will be used as the differential loss(regulariser)\n",
        "X_f = np.expand_dims(np.linspace(-3 * np.pi, 3 * np.pi, 1000), 1)\n",
        "dataset = NumpyDataset(X_f)\n",
        "pinn_model.fit(dataset, nb_epochs=3000)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/deepchem/models/jax_models/pinns_model.py:157: UserWarning: PinnModel is still in active development and we could change the design of the API in the future.\n",
            "  'PinnModel is still in active development and we could change the design of the API in the future.'\n",
            "/usr/local/lib/python3.7/dist-packages/deepchem/models/jax_models/jax_model.py:160: UserWarning: JaxModel is still in active development and all features may not yet be implemented\n",
            "  'JaxModel is still in active development and all features may not yet be implemented'\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.026332732232287527"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xo1Bh059adit",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "outputId": "9b710f09-f7f9-4a2a-c0f1-68bcea71cdb3"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "pinn_output = pinn_model.predict(dataset_test)\n",
        "\n",
        "plt.figure(figsize=(13, 7))\n",
        "plt.plot(test, out_array, color = 'blue', alpha = 0.5)\n",
        "plt.scatter(in_given, out_given, color = 'green', marker = \"o\")\n",
        "# plt.plot(test, nn_output, color = 'red', marker = \"x\", alpha = 0.3)\n",
        "plt.scatter(test, pinn_output, color = 'red', marker = \"o\", alpha = 0.7)\n",
        "\n",
        "plt.xlabel(\"x --> \", fontsize=18)\n",
        "plt.ylabel(\"f (x) -->\", fontsize=18)\n",
        "plt.legend([\"Actual data\" ,\"Supervised Data\", \"PINN\"], prop={'size': 16}, loc =\"lower right\")\n",
        "\n",
        "plt.title(\"Data of our physical system\", fontsize=18)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Data of our physical system')"
            ]
          },
          "metadata": {},
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5vZbMqVAOmdw"
      },
      "source": [
        "# Comparing the results between PINN & Vanilla NN model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "efXAiK0vCXSy",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "outputId": "d2084198-f01f-4953-8c77-95b5f77f28ec"
      },
      "source": [
        "\n",
        "plt.figure(figsize=(13, 7))\n",
        "# plt.plot(test, out_array, color = 'blue', alpha = 0.5)\n",
        "# plt.scatter(in_given, out_given, color = 'green', marker = \"o\")\n",
        "plt.scatter(test, nn_output, color = 'blue', marker = \"x\", alpha = 0.3)\n",
        "plt.scatter(test, pinn_output, color = 'red', marker = \"o\", alpha = 0.7)\n",
        "\n",
        "plt.xlabel(\"x --> \", fontsize=18)\n",
        "plt.ylabel(\"f (x) -->\", fontsize=18)\n",
        "plt.legend([\"Vanilla NN\", \"PINN\"], prop={'size': 16}, loc =\"lower right\")\n",
        "\n",
        "plt.title(\"Data of our physical system\", fontsize=18)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Data of our physical system')"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}